The dynamical RLL conjecture for elliptic L-operators

Let Uq,p([...??]U_{q,p}([...??] be the elliptic quantum algebra with half currents assembled into the LL-operator [...??][...??]. For two auxiliary tensor components, write [...??][...??] and let R+(z1/z2,[...??])R^+(z_1/z_2,[...??]) and R+(z1/z2,[...??])R^{+*}(z_1/z_2,[...??]) denote the corresponding dynamical RR-matrices. Dynamical RLL conjecture. The LL-operator satisfies

R+(12)(z1/z2,[...??])[...??][...??]=[...??][...??]R+(12)(z1/z2,[...??]).R^{+(12)}(z_1/z_2,[...??])[...??][...??]=[...??][...??]R^{+*(12)}(z_1/z_2,[...??]).

This conjecture proposes the exchange relation governing the elliptic LL-operator and is intended to provide its dynamical RLLRLL presentation. The supplied text does not state whether the relation has been proved or remains open.

Sources & referencesView supporting material

Primary source

Hitoshi Konno, “Elliptic Weight Functions and Elliptic q-KZ Equation”, arXiv:1706.07630 (2017).

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